Method for tensioning multiple-strand cables

ABSTRACT

A method whereby the strands ( 13,13 A) are fixed one after another between two cable anchors (A,B) integral with the structure. The method consists: in pulling on one of the ends of a strand ( 13 A) from one (A) of the cable anchors, while the other end is fixed on the other cable anchor (B); continuously testing the tensioning condition of the strand ( 13 A), the condition involving in particular the measured values of the strand tension and of a predetermined parameter. The invention is characterized in that the predetermined parameter is the variation of the distance separating the cable anchors (A,B).

CROSS REFERENCE TO RELATED APPLICATION

This is the 35 USC 371 national stage of International ApplicationPCT/FR01/02775 filed on Sep. 6, 2001, which designated the United Statesof America.

FIELD OF THE INVENTION

The present invention relates to a method for tensioning multiple-strandcables.

Multiple-strand cables can be used in all sorts of civil engineeringstructures, in particular to support structural members with a long span(bridge decks, stadium roofs) or to stabilize slender structures (forexample microwave towers).

Be this as it may, in these types of civil engineering structures, it isnecessary to tension the strands of a cable so that:

a) firstly, the total tension in a cable is uniformly distributedbetween all of the component strands, to prevent dangerous excesstensions in some strands, leading in particular to the risk of ruptureby fatigue,

b) secondly, the tension in the cable as a whole is adjusted to a valueas close as possible to the theoretical value determined when thestructure is designed.

BACKGROUND OF THE INVENTION

FR 2 652 866 describes a method of tensioning a multiple-strand cablewhich ensures a uniform distribution of the tension between all of thestrands (see item a) above). In this method, the first strand, referredto as a witness strand, is installed and tensioned first, and is thenanchored and provided with a measuring cell which indicates the tensionin the witness strand at all times during installation of the cable. Asecond strand is then installed, progressively tensioned, and anchoredat the precise moment that the tension in it is equal to that in thewitness strand. The same procedure is followed for the third strand: itis introduced into the cable and then progressively tensioned until itstension is equal to that of the witness strand. This process continuesuntil the last strand has been tensioned and anchored. The tension inthe witness strand is then released, the measuring cell is removed, andthe witness strand is then tensioned again to the final tensionindicated by the cell.

Consequently, each time that a new strand is introduced into the cable,its tension is set relative to that of the witness strand; the twotensions, which are equal at the time the new strand is anchored, remainequal because they vary in the same manner afterward if the relativeposition of the cable anchors changes:

a) either because of a progressive increase in the tension in the cableas the strands are installed,

b) or because of an external load applied to the structure.

This method, which is known as the isotension method, therefore enablesall of the strands of a cable to be installed with an a priori guaranteeof uniform distribution of the total force in the cable between all thestrands.

It has a number of drawbacks, however.

First of all, the tensions in the new strand and the witness strandremain equal only if the two strands were at the same temperature at themoment of anchoring the new strand. Experience shows that this is notalways the case: the witness strand is contained in a sheath exposed tosunlight and its temperature can be several tens of degrees higher thanthat of the new strand being installed. When the temperatures haveequalized, a relative difference in the values of the tensions in thestrands is then observed, and can exceed 10%. This sometimes requires aretensioning operation, using the method described, to equalize thetensions in the strands, and this represents additional work.

Moreover, although the prior art method imposes the same tension in allthe strands at the time of installing the cable, the problem ofadjusting a cable in accordance with the specifications imposed by thedesign of the structure remain outside the scope of the prior artmethod.

One approach that might be envisaged consists of using stiffnesscharacteristics of the structure to which the cable is fixed to computethe tension to be applied to the first strand so that at the end of theinstallation of the strands the tension in the cable reaches a specifictotal. However, experience shows that this approach is imprecise,because of uncertainties as to the real load on the first strand, suchas the real conditions of contact of the sheath, the presence of endtubes temporarily supported by the strand, etc. In practice, thisproblem is overcome by proceeding in two stages:

-   -   the strands are initially installed as previously described at a        fraction of the final tension (from 60% to 90%, depending on the        project),    -   appropriate means are then used to compute the stretch to be        imparted to all of the strands to achieve the final tension,        this computation yielding reliable results since it is        reasonable to assume that the weight of the sheath is uniformly        distributed between all of the strands; the calculated stretch        is then usually applied to the witness strand, after which the        other strands are retensioned using the isotension method.

It is obvious that this two-fold process greatly complicates the workand therefore increases the cost associated with installing andadjusting a cable.

Finally, the prior art method requires the tension in the witness strandto be released at the end of the work, followed by demounting themeasuring cell and retensioning the witness strand to the previouslymeasured tension; this also complicates the work.

SUMMARY OF THE INVENTION

An object of the invention is to provide a method of tensioning amultiple strand cable that is free of the drawbacks of the prior arttechnique.

The invention therefore provides a method of tensioning a multiplestrand cable in which said strands are installed one after the otherbetween two cable anchors fastened to the structure, the methodconsisting of:

-   -   pulling on one end of a strand from one of the cable anchors        with the other end fixed to the other cable anchor,    -   measuring continuously the value of the tension in the strand,        and    -   continuously testing a condition for ending tensioning for the        strand, said condition employing an expression that is a        function of a predetermined parameter,    -   which method is characterized in that said predetermined        parameter is the variation in the distance between said cable        anchors.

Thanks to the above features, it becomes possible:

-   -   to ensure a uniform distribution of the total tension in the        cable between all the strands, even if they are at different        temperatures during installation,    -   to impose on the cable as a whole a tension as close as possible        to that specified when the structure is designed, even if the        real loading conditions for the structure differ from those        allowed for in the computations for the phase concerned, and    -   to eliminate the intermediate stages of retensioning strands        imposed by the prior art technique.

According to other advantageous features of the invention, the methodfurther consists in:

a) determining the theoretical value of the zero tension length of thecable as a function of:

-   -   the total number of strands of the cable, the axial stiffness        and the weight per unit length of each of the strands of the        cable,    -   the theoretical position of the cable anchors as defined by the        drawings of the structure,    -   the tension in the cable and the displacements of the cable        anchors predicted by the design computations for the structure        for a predetermined reference phase occurring after tensioning        the cable,

b) evaluating the initial displacements of the cable anchors immediatelybefore installing the first strand of the cable,

c) during the tensioning of each strand of the cable:

-   -   measuring continuously said distance variation from the step b),    -   executing a computation loop to test continuously the condition        for ending tensioning the strand, using said expression which is        a function of said predetermined parameter, and

d) locking the strand being tensioned to the cable anchor as soon as thecondition for ending tensioning of the strand is satisfied.

There are essentially two embodiments of a method according to theinvention.

In a first embodiment: said expression which is a function of saidpredetermined parameter defines the stretch remaining to be applied tothe strand until the condition for ending tensioning is satisfied.

In this case, said expression can be defined by the followingparameters:

i) the stiffness and the weight per unit length of the strand,

ii) the theoretical zero tension length,

iii) said initial displacements,

iv) the tension measured in the strand, and

v) said distance variation,

and the strand is locked when the stretch remaining to be applied isequal to zero.

It may then be preferable if said expression is also defined by a valuerepresenting the insertion of the keys by which said strand is anchoredto its cable anchor.

In the second embodiment, said expression which is a function of saidpredetermined parameter can define the locking tension that said strandmust reach before it can be anchored.

In this case, said expression is defined by the following parameters:

i) the stiffness and the weight per unit length of the strand,

ii) the theoretical zero tension length,

iii) said initial displacements,

iv) said distance variation,

and the strand is locked when the measured value of the tension appliedto said strand becomes equal to that of the tension calculated in thisway.

According to other features of the method applying to both embodimentsas defined above:

-   -   said initial displacements are measured on the structure by a        procedure taking account of the construction tolerances of said        structure or are determined from the results of design        computations for the structure;    -   the cable includes a protective sheath and the method further        consists of:    -   i) determining the theoretical zero tension length from the        weight per unit length of said sheath, and    -   ii) during the computation relating to said condition for ending        tensioning, increasing the weight per unit length of the strand        being tensioned by a fraction of the weight per unit length of        the sheath;    -   the method also consists of taking account of the temperature of        the strand being tensioned during step c) in the computation        relating to said condition for ending tensioning;    -   the method also consists of taking account of the temperatures        of the cables already installed on the structure and of the        structure itself during step b) in the determination of said        initial displacements.

BRIEF DESCRIPTION OF THE DRAWINGS

Other features and advantages of the present invention will becomeapparent in the course of the following description, which is given byway of example only and with reference to the accompanying drawings, inwhich:

FIG. 1 is a diagram explaining how various concepts used during theexecution of a tensioning method according to the invention are defined;

FIG. 2 is a highly simplified representation of an installation fortensioning a cable;

FIG. 3 is a flowchart showing computation steps of a first embodiment ofa method according to the invention;

FIG. 4 is a flowchart showing computation steps of a second embodimentof a method according to the invention; and

FIG. 5 shows one embodiment of apparatus for measuring the variation inthe distance between cable anchors that can be used in a methodaccording to the invention.

DETAILED DESCRIPTION OF THE INVENTION

The following description of a preferred embodiment of a methodaccording to the invention relates to a structure on which cables mustbe installed that takes the form of a suspension bridge whose supporteddeck is constructed by successive cantilevering, a situation in whichthe method is particularly beneficial. Nevertheless, it is expresslyspecified here that the method is not limited to this particularsituation and that any structure involving the installation andtensioning of multiple strand cables may constitute an application of amethod according to the invention.

The FIG. 1 diagram shows from the side a symmetrical suspension bridgecomprising two pylons 1 and 2 and a deck 3 which rests on piles 4 in thelateral spans 5 and 6. In the central span, i.e. between the two pylons,the deck 3 is constructed by successive cantilevering, and the lateralspans 5 and 6 can be constructed in parallel with the construction ofthe central span, using the same technique, or constructed beforehand,using a different method (on an arch, timed shifting). Be this as itmay, and without compromising the general applicability of theinvention, the examples concern the tensioning of a central span cable,all the cables anchored to a pylon being installed in aquasi-symmetrical fashion to guarantee the stability of the pylon. Thediagram shows a few cables 7, 8, 9, 10 and 11.

The portion 3A of the central span is deformed by its own weight, by theaction of the cables that support it, and by the effect of any siteloads (mobile crews, plant, handling machinery, etc.). The deformationis greatly exaggerated in FIG. 1, of course.

It is assumed that during the next phase of the construction of thestructure a new cable 12 (not shown in FIG. 1) is to be installedalongside the cable 8 and tensioned using a method according to theinvention.

The following description of a tensioning method refers to the conceptof “displacement” used by persons skilled in this art. In this context,the “displacement” of a point M of a structure in a given state is equalto a vector {right arrow over (P₀P)}, where P₀ is the position of thepoint M in an original state of the structure and P is the position ofthe point M in the state under consideration.

In the context of computing expressions operative in the condition forterminating tensioning a strand in a method according to the invention,any convention can be adopted as to the definition of the origin of thedisplacement of a cable anchor; once defined, that origin then appliesthroughout the computation process.

The following description of a method according to the invention alsorefers to the concept of the “zero tension length” of a cable or strand,which theoretically characterizes the tension in an installed cable. Thezero tension length L of an installed strand is defined as the lengththat that strand would have if it were cut at its cable anchors andmeasured when held straight with negligible tension. It is because thezero tension length L of a cable is less than the straight line distanced between its cable anchors that the cable can develop a tension T,which has a vertical component V balancing the weight of thecorresponding section of deck. By judiciously choosing the zero tensionlength of each cable of a structure, the structure is tensioned so thatthe loads on it during construction and in service remain permissible,even if this means repeating the tensioning at certain phases ofconstruction. As already indicated, the strand is tensioned by pullingon its end adjacent the active cable anchor A by means of a jack 15 (seeFIG. 2): any stretching of the strand Δl by the jack produces acorresponding reduction Δl of its zero tension length L.

FIG. 1 shows some of the basic concepts that apply to the embodiment tobe described of a method according to the invention:

-   -   the profile (O) represented in chain-dotted line is the profile        of the structure from which the displacements are measured;    -   the profile (R_(pr)) represented in full line is the profile        associated with a predetermined reference phase; the reference        state defines the required tension in the cable at the end of        the tensioning operation; at this stage no attempt is made to        achieve a given tension, which would then be dependent on site        loads, whose intensity and position cannot be predicted        accurately beforehand; to the contrary, the computations        effected by the computer employed for this purpose seek to        impose a tension in the cable such that if, in the reference        state, the cable anchors actually have the displacements        predicted by the design computations, then the tension in the        cable in said reference state is also that predicted by the        design computations. It is important to note that the values,        relating to the reference state, of the tension in the cable and        the displacements of the cable anchors taken into account in the        computations, are theoretical values taken directly from the        design computations, and therefore constitute, as it were,        specifications imposed on the on-site construction work by the        designers;    -   the profile (l) represented in full line is associated with the        phase of measuring the initial displacements of the cable        anchors;    -   {right arrow over (μ)}A_(pr) is the displacement of the bottom        cable anchor A considered in the predetermined reference phase;    -   {right arrow over (μ)}A₁ is the initial displacement of the        cable anchor A;    -   {right arrow over (χ)}A₀ is the position vector {right arrow        over (OA₀)} of the cable anchor A from which the displacements        are measured, O designating the origin of the system of axes        Oxyz relative to which the structure is described.

Of course, analogous vectors {right arrow over (μ)}B_(pr), {right arrowover (μ)}B₁ and {right arrow over (χ)}B₀ are assigned to the top cableanchor B.

From now on the description refers to FIG. 2, which shows the cable 12in profile during its installation between its two cable anchors A andB, respectively on the deck portion 3A and the pylon 1. The structure ofthese cable anchors can be that described in the French patentpreviously cited. The cable anchor A is that incorporating the anchorjaws or keys by means of which the active end of each strand is attachedto the cable anchor. The top cable anchor B is “passive”.

The cable 12, and all the other cables already installed or yet to beinstalled, comprise a plurality of strands 13, the number of which, inpractice, routinely varies from 30 to 80, for example, and their lengthcan be 250 meters or more. Moreover, in the embodiment described, eachcable has a protective sheath 14 surrounding all the strands 13. Thesheath 14 is disposed between the cable anchors A and B at the same timeas installing the strand that will be tensioned first for the cableconcerned, but is not fixed to them. The sheath is therefore threadedover the first strand and all the other strands of the same cable arethen threaded into the sheath before they are anchored.

In some structures, however, it is possible to dispense with a sheatharound the strands provided that they are sufficiently protectedindividually against the risks of corrosion.

In FIG. 2, four strands 13 have already been installed and tensioned anda fifth strand 13A has been threaded into the sheath 14 and anchored tothe top cable anchor B and is therefore in the process of beingtensioned.

To this end, a tensioning jack 15 known in the art is mountedtemporarily on the strand 13A. The jack is associated with a sensor 15Afor measuring the traction force that it applies to the strand 13A.

The device for implementing this method according to the inventionincludes, in addition to the jack 15, a microcomputer 16 storing in theform of files in a permanent memory 17 all the data concerning thecables to be installed on the structure.

According to the invention, the microcomputer 16 is connected to thesensor 15A of the jack 15 and also to means for measuring the distancebetween the cable anchors A and B adapted to measure the variation inthe distance between them as each strand 13, 13A is tensioned. In thesituation represented, the measuring means comprise a laser rangefinder18 fixed to the structure near the cable anchor A and a reflector 19which reflects the measuring laser beam emitted by the rangefinder 18.These rangefinders are well known to the person skilled in the art.

The microcomputer 16 is also connected to a temperature sensor 20 formeasuring the temperature of the strand being tensioned. Themicrocomputer 16 is further connected to another sensor 22 whichmeasures the temperature inside a witness cable section 21. This witnesssection, consisting of a bundle of strands and a sheath membersurrounding them, is suspended or otherwise disposed above the deckportion 3A in the vicinity of the cables already installed. This meansthat the temperature inside the sheath of the cables already installedcan be determined without having to pierce the sheath to insert asensor.

Referring from now on to FIG. 3, the computation algorithm used by themicrocomputer 16 to execute a first embodiment of a method according tothe invention using data supplied to it by the tension sensor 15A, thepermanent memory 17, the rangefinder 18 and the temperature sensor 20 isdescribed. It is assumed that, using an appropriate topographicalprocedure, it has been possible to measure on site the effective valuesof the displacements {right arrow over (μ)}A_(r) and {right arrow over(μ)}B_(t) of the cable anchors, just before installing the first strand.If this is not the case, it is always possible to use theoretical valuesof these displacements taken into account in the design process for thisphase, provided that the predicted loading is rigorously respected onsite and these values are corrected by means of a computer, thecorrections being necessary because the temperatures of the structureand the cables already installed generally differ from the theoreticalvalues taken into account during the design computations (whence thebenefit in this situation of the temperature sensor 22).

In the context of this first embodiment, it is assumed that thecondition for ending tensioning of the strand is expressed by taking asa control parameter the remaining stretch Δl to be applied to thestrand: pulling on the active end of the strand ceases when this stretchbecomes equal to zero.

However, another embodiment is described hereinafter in which thecontrol parameter is the tension indicated by the sensor 15A; in thiscase, the condition for ending tensioning of the strand is reached whenthe tension in the strand being installed reaches a particular blockingvalue computed by the microcomputer 16 as a function of measurements andstored data.

Note, however, that the first embodiment has the advantage that it cantake directly into account in the tensioning procedure the systematicrelaxation effect that is a feature of some other devices when thetensioning jack 15 is released, known to persons skilled in the art as“key entry”.

However, regardless of the method chosen, at the end of the designprocess data is available for computing the theoretical value of thezero tension length L_(th) of each cable to be installed. Thecomputation is based on the following data (see FIGS. 3 and 4, step S1):

-   -   the theoretical positions {right arrow over (χ)}A₀ and {right        arrow over (χ)}B₀ of the cable anchors A and B from which the        displacements are measured,    -   the theoretical values, obtained from the design computations,        of the tension T_(pr) of the cable and the displacements {right        arrow over (μ)}A_(pr) and {right arrow over (μ)}B_(pr) of its        cable anchors A and B for the predetermined reference phase,    -   the axial stiffness EA of the cable, obtained by multiplying the        number of strands n constituting the cable by the apparent        Young's modulus E of a strand and by the section a of a strand:        EA=nEa    -   the weight per unit length q of the cable, given by the equation        q=q_(g)+nq_(t), q_(g), where q represents the weight per unit        length of the sheath 14 and q_(t) the unit length of a strand.

To compute the value of L_(th), it is necessary to solve the followingapplied mechanics problem: “Given two points A and B in space whoserelative position is characterized by the vector {right arrow over(AB)}={right arrow over (AB_(pr))}=({right arrow over (χ)}B₀+{rightarrow over (μ)}B_(pr))−({right arrow over (χ)}A₀+{right arrow over(μ)}A_(pr)) axial stiffness EA and of weight per unit length q,determine the untensioned length L of said cable so that, once anchoredat A and B, it exerts at the point A a force equal to a given valueT_(A)”. The classical elastic chain theoretical model is used toestablish the equations needed to solve this problem. This model isdescribed in “Cable Structures” by H. Max Irvine, published in 1981 byThe MIT Press Series in Structural Mechanics, pages 16 to 20.Symbolically, the theoretical zero tension length L_(th) of the cable isa function of EA, q, {right arrow over (AB)}_(pr) and T_(pr):L _(th)=Λ(EA, q, {right arrow over (AB)} _(pr) , T _(pr))

In both embodiments, the method of tensioning a cable begins with thedetermination of the initial displacements {right arrow over (μ)}A_(r)and {right arrow over (μ)}B_(t) of the cable anchors (see FIGS. 3 and 4,step S2), which can essentially be obtained in two ways:

-   -   either they are measured on the structure by methods known in        the art of geometrical tracking of the pylon 1 and the deck 3A,    -   or they are estimated from corresponding theoretical values        extracted from the design computations and stored in the        permanent memory 17.

In the latter case, a real load must be imposed on the structure that isas close as possible to that used in the design computations, inparticular with regard to site loads (plant, lifting machinery, etc.).Moreover, in this case, the raw theoretical values must be corrected totake account of the fact that neither the cables already installed northe remainder of the structure is at the uniform constructiontemperature used in the design computations. The corrective computationis effected by reading a value representative of the temperature of allof the installed cables by means of the sensor 22 and entering anaverage value for the temperature of the remainder of the structure; thecomputer 16 then carries out the necessary computations based on unitarythermal load situations determined during the design computations andstored in the permanent memory 17.

In the following description, only this first situation is considered,and applied to both of the embodiments described.

Once the initial displacements of the cable anchors have been determinedin step S2, there follows the threading and tensioning of each of thestrands of the cable.

The following operations of the method according to the invention areexecuted each time that a strand 13 is tensioned.

In a first embodiment shown in FIG. 3, during tensioning (for example ofthe strand 13A), the computer 16 executes repetitively (in step S3, forexample at intervals of one second) a computation to determine thestretch Δl that remains to apply to the strand 13A before the jack 15 isreleased and the strand 13A is anchored by inserting the keys into thecable anchor. The data that has to be measured or determined on site forthis computation comprises:

-   -   the initial displacements {right arrow over (μ)}A_(t) and {right        arrow over (μ)}B_(t) previously determined (step S2),    -   the tension T in the strand measured by means of the sensor 15A,    -   the variation Δd of the straight line distance between the cable        anchors A and B measured using the rangefinder 18, the origin of        Δd being taken at the time when the initial displacements are        determined, i.e. just before threading the first strand 13,    -   the temperature θ_(tor) of the strand 13A measured by the sensor        20,    -   the insertion of the keys rc.

As tensioning proceeds, the stretch Δl remaining to be applied to thestrand 13A is displayed on the screen of the microcomputer 16 and asignal can be sent to an automaton 23 controlling the jack 15 to releasethe latter as soon as Δl reaches the value zero, allowing for theinsertion of the keys rc.

At a given moment in tensioning the strand 13A, its zero tension lengthL is obtained from a function analogous to that used to compute thetheoretical length previously described:L=Λ(Ea, q*, {right arrow over (AB)}, T)where:

-   -   Ea is the axial stiffness of the strand,    -   q* is the weight per unit length q_(t) of the strand weighted by        the contribution of the strand to supporting the weight per unit        length q_(g) of the sheath 14:        q*=q _(t) +q _(g) /i (i is the number of the strand)    -   {right arrow over (AB)} represents the relative position of the        cable anchors, if they were perfectly installed:        {right arrow over (AB)}=({right arrow over (χ)}B ₀ +{right arrow        over (μ)}B ₁)−({right arrow over (χ)}A ₀ +{right arrow over        (μ)}A ₁)+{right arrow over (I)}Δd        where {right arrow over (I)} is the unit vector linking the        cable anchors A and B.

The zero tension length L_(θ), the objective to be achieved at the endof the tensioning operation, at a temperature θ_(tor), has the value:L _(θ) =L _(th)[1+□(θ_(tor)−θ_(th))]where designates the coefficient of expansion of the strand.

The stretch Δl remaining to be applied to the strand 13A beforereleasing the jack 15 is finally given by the equation:Δl=L−L _(θ) +rcin which rc designates the insertion of the keys (which is of the orderof 4 to 7 mm in practice).

The strand 13A is then anchored permanently in the cable anchor A andthe jack 15 is detached from it so that it can be used for the nextstrand 13.

As shown in FIG. 4, in a second embodiment of the invention, steps S1and S2 are executed in the same way as in the first embodiment.

The second embodiment differs in the step S3, during which, instead ofcomputing the stretch value Δl, a value T is computed representing thelocking tension to be achieved in the strand 13A before anchoring cantake place.

The locking tension T_(bloc) is determined from the values {right arrowover (AB)}, q* and L_(θ) using the following equation:T _(bloc) =T(Ea,q*,{right arrow over (AB)},L _(θ))

Note that the determination of the function T above can use the sameelastic chain theory as described in the work previously cited, theproblem to be solved being based on looking for the value T rather thanthe value of L.

The value of the locking tension T_(bloc) computed by the computer 16 isdisplayed in a window V2 of the screen and the real value of the tensionin the strand 13A measured by means of the sensor 15A is displayedsimultaneously in another window V1. Locking is effected as soon as thevalues in the windows V1 and V2 are equal. The process can be stoppedautomatically by the automaton 23 as soon as the condition of equalityapplies.

FIG. 5 shows a variant of the rangefinder 18A for measuring thevariation of the distance between the cable anchors A and B and whichcan also be used to execute the method according to the invention. Inthis case, an Invar® wire 24, for example, is fixed at one end to thepylon 1 in the vicinity of the top cable anchor B. The other end of thewire 24 passes over a pulley 25 mounted in the vicinity of the bottomcable anchor A and is attached to a weight 26. An electronic comparator27 on the portion 3A of the deck under construction measures thevariation of the vertical position of the weight 26 in order to deducetherefrom the variation in the distance between the cable anchors A andB.

Other variants can be considered of the device used to measure thedistance variation between the cable anchors A and B. Thus using anoptonumerical system enables the evolution of the distance between atarget and the instrument to be determined by means of digital imagingprocessing in real time.

1. A method of tensioning a multiple strand cable in which said strandsare installed one after the other between two cable anchors fastened toa structure, the method comprising the steps of: pulling on one end of astrand from one of the cable anchors with the other end fixed to theother cable anchor, measuring continuously the value of the tension inthe strand, and continuously testing a condition for ending tensioningfor the strand, said condition employing an expression that is afunction of a predetermined parameter, wherein said predeterminedparameter is the variation in the distance between said cable anchors.2. A tensioning method according to claim 1, further comprising thesteps of: a) determining the theoretical value of the zero tensionlength of the cable as a function of: the total number of strands of thecable, the axial stiffness and the weight per unit length of each of thestrands of the cable, the theoretical position of the cable anchors asdefined by drawings of the structure, the tension in the cable and thedisplacements of the cable anchors predicted by design computations forthe structure for a predetermined reference phase occurring aftertensioning the cable, b) evaluating the initial displacements of thecable anchors immediately before installing the first strand of thecable, c) during the tensioning of each strand of the cable: measuringcontinuously a distance variation from step b), executing a computationloop to test continuously the condition for ending tensioning thestrand, using said expression which is a function of said predeterminedparameter, and d) locking the strand being tensioned to the cable anchoras soon as the condition for ending tensioning of the strand issatisfied.
 3. A tensioning method according to claim 2, wherein saidexpression which is a function of said predetermined parameter definesthe stretch remaining to be applied to the strand until the conditionfor ending tensioning is satisfied.
 4. A tensioning method according toclaim 3, wherein said expression is defined by the following parameters:i) the stiffness and the weight per unit length of the strand, ii) thetheoretical zero tension length, iii) said initial displacements, iv)the tension measured in the strand, and v) said distance variation, andin that the strand is locked when the stretch remaining to be applied isequal to zero.
 5. A tensioning method according to claim 4, wherein saidexpression is also defined by a value representing an insertion of keysby which said strand is anchored to its cable anchor.
 6. A tensioningmethod according to claim 2, wherein said expression which is a functionof said predetermined parameter defines the locking tension that saidstrand must reach before it can be anchored.
 7. A tensioning methodaccording to claim 6, wherein said expression is defined by thefollowing parameters: i) the stiffness and the weight per unit length ofthe strand, ii) the theoretical zero tension length, iii) said initialdisplacements, iv) said distance variation, and wherein the strand islocked when the measured value of the tension applied to said strandbecomes equal to that of the tension calculated in this way.
 8. A methodaccording to claim 2, wherein said initial displacements are measured onthe structure by a procedure which factors in construction tolerances ofsaid structure.
 9. A tensioning method according to claim 2, whereinsaid initial displacements are determined from the results of designcomputations for the structure.
 10. A tensioning method according toclaim 2, wherein the cable includes a protective sheath and the methodfurther comprises: i) determining the theoretical zero tension lengthfrom the weight per unit length of said sheath, and ii) during thecomputation relating to said condition for ending tensioning, increasingthe weight per unit length of the strand being tensioned by a fractionof the weight per unit length of the sheath.
 11. A tensioning methodaccording to claim 2, further comprising factoring in the temperature ofthe strand being tensioned during step c) in the computation relating tosaid condition for ending tensioning.
 12. A tensioning method accordingto claim 2, further comprising factoring in the temperatures of thecables already installed on the structure and of the structure itselfduring step b) in the determination of said initial displacements.